Here are a few we've done in a dialogue fashion:

FOOLISH QUESTIONS
BUFFALO BOY
THE BALLAD OF ERICA LEVINE
ARKANSAS TRAVELER (more of a story than a song)
BILLY BOY
CAPTAIN WEDDERBURN'S COURTSHIP
THE HOUSEWIFE'S LAMENT
ON ILKLA MOOR BAHT 'AT

Also, some old country songs have choruses with two parts that have different words such as "Where the Soul of Man Never Dies" [see TO CANAAN'S LAND I'M ON MY WAY] and "WHISPERING HOPE".

Finally, Larry Mohr and Odetta put together something they called "Just the Facts, Ma'am" in which one of them sang "I WAS BORN ALMOST TEN THOUSAND YEARS AGO" and the other sang "THE BIGGEST THING THAT MAN HAS EVER DONE". They alternated verses and then, at the end, sang the last verses together. Even though they were singing two different songs, they blended perfectly. "Just the Facts, Ma'am" appeared in an ancient issue of Sing Out! and in "Reprints from Sing Out! Volume Four".

Bev and Jerry